Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees
نویسندگان
چکیده
منابع مشابه
Randomized Incremental Construction of Abstract Voronoi Diagrams
Abstract Voronoi diagrams were introduced by R . Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis ofVoronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages over previous algorithms: • It can handle...
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We present an incremental algorithm for constructing and reconstructing Generalized Voronoi Diagrams (GVDs) on grids. Our algorithm, Dynamic Brushfire, uses techniques from the path planning community to efficiently update GVDs when the underlying environment changes or when new information concerning the environment is received. Dynamic Brushfire is an order of magnitude more efficient than cu...
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We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of n sites in the plane as sites are added to the set. To that effect, we define a general update operation for planar graphs that can be used to model the incremental construction of several variants of...
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Abstract Voronoi diagrams were introduced by R. Klein (1988) as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor’s randomized incremental construction technique (1989). The new algorithm has the following advantages over previous algorithms: l It can handle a much wider cl...
متن کاملIncremental Construction of the Generalized Voronoi Diagram, the Generalized Voronoi Graph, and the Hierarchical Generalized Voronoi Graph
1 Overview This work introduces a new incremental construction procedure for the generalized Voronoi diagram (GVD), the locus of points equidistant to two obstacles. This procedure is incremental in that it requires line of sight information (see Figure 4) to construct the GVD. Note that this notion of incremental is di erent from previous de nition of incremental where the GVD is constructed b...
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ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2014
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2014/456739